An important step in data analysis is data exploration and representation. In this tutorial we will see how by combining a technique called Principal Component Analysis (PCA) together with Cluster Analysis we can represent in a two-dimensional space data defined in a higher dimensional one while, at the same time, being able to group this data in similar groups or clusters and find hidden relationships in our data. More concretely, PCA reduces data dimensionality by finding principal components. These are the directions of maximum variation in a dataset. By reducing a dataset original features or variables to a reduced set of new ones based on the principal components, we end up with the minimum number of variables that keep the maximum amount of variation or information about how the data is distributed. If we end up with just two of these new variables, we will be able to represent each sample in our data in a two-dimensional chart (e.g. a scatterplot). As an unsupervised data analysis technique, clustering organises data samples by proximity based on its variables.

As the Primary season progresses there's been no end of political pundits backpedaling and mea-culpa-ing over their previous inability to predict the rise of Donald Trump to become the frontrunner in the GOP. From Charles Krauthammer admitting that it was wrong to laugh at The Donald to innumerable others, both liberal and conservative, wishing they'd take Trump seriously, it seems like just about everyone in the Predictive Class will be dining on roast crow this Easter. But why did they get things so wrong? Was it because they assumed that he'd "crash and burn" like John Podhoretz did? Was it because they assumed that he couldn't win because Republican voters hated him, as implied by Patrick Murray of Monmouth University when releasing early poll results in June of 2015?

The problem of recovering a structured signal $\mathbf{x} \in \mathbb{C}^p$ from a set of dimensionality-reduced linear measurements $\mathbf{b} = \mathbf {A}\mathbf {x}$ arises in a variety of applications, such as medical imaging, spectroscopy, Fourier optics, and computerized tomography. Due to computational and storage complexity or physical constraints imposed by the problem, the measurement matrix $\mathbf{A} \in \mathbb{C}^{n \times p}$ is often of the form $\mathbf{A} = \mathbf{P}_{\Omega}\boldsymbol{\Psi}$ for some orthonormal basis matrix $\boldsymbol{\Psi}\in \mathbb{C}^{p \times p}$ and subsampling operator $\mathbf{P}_{\Omega}: \mathbb{C}^{p} \rightarrow \mathbb{C}^{n}$ that selects the rows indexed by $\Omega$. This raises the fundamental question of how best to choose the index set $\Omega$ in order to optimize the recovery performance. Previous approaches to addressing this question rely on non-uniform \emph{random} subsampling using application-specific knowledge of the structure of $\mathbf{x}$. In this paper, we instead take a principled learning-based approach in which a \emph{fixed} index set is chosen based on a set of training signals $\mathbf{x}_1,\dotsc,\mathbf{x}_m$. We formulate combinatorial optimization problems seeking to maximize the energy captured in these signals in an average-case or worst-case sense, and we show that these can be efficiently solved either exactly or approximately via the identification of modularity and submodularity structures. We provide both deterministic and statistical theoretical guarantees showing how the resulting measurement matrices perform on signals differing from the training signals, and we provide numerical examples showing our approach to be effective on a variety of data sets.

This paper tackles the problem of endogenous link prediction for knowledge base completion. Knowledge bases can be represented as directed graphs whose nodes correspond to entities and edges to relationships. Previous attempts either consist of powerful systems with high capacity to model complex connectivity patterns, which unfortunately usually end up overfitting on rare relationships, or in approaches that trade capacity for simplicity in order to fairly model all relationships, frequent or not. In this paper, we propose Tatec, a happy medium obtained by complementing a high-capacity model with a simpler one, both pre-trained separately and then combined. We present several variants of this model with different kinds of regularization and combination strategies and show that this approach outperforms existing methods on different types of relationships by achieving state-of-the-art results on four benchmarks of the literature.

We represent knowledge as integrity constraints in a formalization of probabilistic spatio-temporal knowledge bases. We start by defining the syntax and semantics of a formalization called PST knowledge bases. This definition generalizes an earlier version, called SPOT, which is a declarative framework for the representation and processing of probabilistic spatio-temporal data where probability is represented as an interval because the exact value is unknown. We augment the previous definition by adding a type of non-atomic formula that expresses integrity constraints. The result is a highly expressive formalism for knowledge representation dealing with probabilistic spatio-temporal data. We obtain complexity results both for checking the consistency of PST knowledge bases and for answering queries in PST knowledge bases, and also specify tractable cases. All the domains in the PST framework are finite, but we extend our results also to arbitrarily large finite domains.

The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, namely their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the robustness of classifiers to adversarial perturbations, and show fundamental upper bounds on the robustness of classifiers. Specifically, we establish a general upper bound on the robustness of classifiers to adversarial perturbations, and then illustrate the obtained upper bound on the families of linear and quadratic classifiers. In both cases, our upper bound depends on a distinguishability measure that captures the notion of difficulty of the classification task. Our results for both classes imply that in tasks involving small distinguishability, no classifier in the considered set will be robust to adversarial perturbations, even if a good accuracy is achieved. Our theoretical framework moreover suggests that the phenomenon of adversarial instability is due to the low flexibility of classifiers, compared to the difficulty of the classification task (captured by the distinguishability). Moreover, we show the existence of a clear distinction between the robustness of a classifier to random noise and its robustness to adversarial perturbations. Specifically, the former is shown to be larger than the latter by a factor that is proportional to \sqrt{d} (with d being the signal dimension) for linear classifiers. This result gives a theoretical explanation for the discrepancy between the two robustness properties in high dimensional problems, which was empirically observed in the context of neural networks. To the best of our knowledge, our results provide the first theoretical work that addresses the phenomenon of adversarial instability recently observed for deep networks. Our analysis is complemented by experimental results on controlled and real-world data.

Here are choice articles on hot leadership topics culled from the business schools, the business press and major consulting firms, to start off your work week. Highlights include leading in the digital age, changing the game in industrial goods through digital services, the rise of machine learning, how women and men internalise the glass ceiling, and the explosion of wearing work on our wrists. Note: Some links require you to register or are to publications that have some form of limited paywall. "Servant leadership is not a new concept. Robert Greenleaf introduced the idea back in 1977. In recent years, however, concrete evidence has emerged that the approach delivers more than warm, fuzzy feelings. Last month, the first quantitative study that begins to explain a connection between servant leadership and improved individual performance was published by researchers in Canada. This new evidence may help move servant leadership from a niche practice to one adopted by more executives."

Machine learning is becoming a buzzword, everybody talks aboit it and few seem to be interested in the math underneath (I find statements like "I wanted to know more but all sources were too statistical/mathematical and I wanted more practical stuff"). Let me tell you something: You can't really use Machine Learning if you don't know the statistical/mathematical basis. I am really upset when I see a Youtube video of some guy in T-Shirt probably working at a large organization ranting about Machine Learning and Data Science, telling programmers that maths is easy to grasp. Everybody knows how to press a button or, if you force me, almost everybody knows how to fix something in their Windows control panel, but that does not mean we can trust them when talking about building a secure payment system, Everybody can use Mahout or the like but that does not mean he knows jack about what he is doing using Naive Bayes to predict the class from thre variables (x, y, z) where z x 2 and x belongs to the range [-1,1]. Machine Learning is just a fancy word for the statistical/mathematical tools lying underneath, whose objective is to extract something that we may loosely call knowledge (or something that we understand) from data (or something chaotic that we do not understand), so that computers may take action based on the inferred knowledge.

Office work is also set to change. Earlier this week, Blue Prism announced plans to debut on the London Stock Exchange. The company, which grew 35 percent in 2015, develops "software robots" which can perform clerical and administration tasks. "Software robots have been deployed successfully and strategically by large, blue chip organizations that have derived tremendous value from this new solution to the labor market," said Alastair Bathgate, the company's co-founder and CEO, in a press release. However, workers should not be overly worried.

Artificial intelligence or AI is the future of the legal profession. The good news for anyone worried by that statement is people have been making it for several decades. The first international conference on law and artificial intelligence was held in Boston in 1987, before the invention – let alone the mass use of – the worldwide web. Despite the early enthusiasm the concept of computers taking over legal reasoning tasks from human lawyers has yet to become reality. Partly this is because artificial intelligence developed more slowly everywhere than the enthusiasts predicted.